Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

PID control in the presence of static friction: exact and describing function analysis

Abstract: PID position control in the presence of static friction is shown to lead to a frictional limit cycle for all stabilizing combinations of P, I and D parameters. An idealized Coulomb+static friction model, dimensional analysis and the study of all possible solutions to the differential equations are used to achieve analytic results for this nonlinear problem. Three theorems establishing the predictions of the describing function are also presented.

Stability Analysis of the Shunt Regulator With Nonlinear Controller in PCU Based on Describing Function Method

Abstract: The shunt regulator is a key part of the power conditioning unit, which is becoming more and more important in the spacecrafts. Due to the nonlinear link, the switch operating with hysteresis control, the shunt regulator is a nonlinear system; however, the stability analysis method for the system is still grounded on the approximate linearization method, which neglects some of the ac and dc characteristics. In this paper, a novel stability analysis method for the nonlinear systems is proposed based on the describing function, which can be used to model the nonlinear link in the shunt regulator system. Further, the different conclusion of the shunt regulator system stability are drawn, by the approximate linearization method and the stability analysis method proposed in this paper, respectively. Finally, the simulation and experimental results prove the correctness of the stability analysis method with describing function and discover the incompletion of the approximate linearization methods on the stability analysis. Therefore, this paper provides a new way to analyze the stability of the nonlinear systems.

On the Limits of Manual Control

Abstract: Theoretical predictions and experimental data for the limits of manual control of unstable oscillatory second-order controlled elements are presented. At the limits of manual control, amplitude distributions of the system error and operator output were nearly Gaussian. The quasi-linear describing function model of the human operator implied from analysis of the experimental measurements indicates that the operator was capable of generating equalization equivalent to a double lead and that, for certain controlled elements, he adopted a response behavior analogous to quasiprecognitive tracking with a compensatory display.

A study of a system of current fed converters as an active three phase filter

Abstract: Three single phase current fed converters operating in pwm mode, are combined as an active power filter of 15 kVA. The undesired limit cycle shown by the system is eliminated by feedback loop compensation. Analog, computer and analytical models which predict remarkably similar system responses are used to investigate the technique. The analytical model involves describing function methods. The losses in the converters are modelled, and used as a feedback reference to allow losses in the system to be accurately covered from the supply. The system behaves as an accurate, fast active filter for distortion in power networks. Results illustrating this include a comparison between the system response without control loop compensation and that with control loop compensation. This is shown for the computer simulation as well as the practical system. Some more results include the response of the system to both a balanced and an unbalanced set of references in the three phases. The last results shown, illustrate the ability of the system to compensate a non-linear load.